This is the last teaching lesson for this semester, we finish off Chapter 14 for Algebraic Manipulations.

Today we talked about simplifying algebraic fractions, fractions whose numerator and denominator are both polynomials — such expression is also called rational expression. We can eliminate the common factors. We talk about how to solve equations with algebraic fractions — such equation is also called rational equation. One important thing to remember when solving a rational equation is that any solution cannot make any denominator zero.

We talk about identity equations where it is true for all values for the variable involved.

We will have a review next week, followed by a final exam in two weeks (last day of school).

Homework: Page 148, #20 – 22, 26 – 32.

As it turns out, the school has designated next week (6/15) as the exam day, so we will have our exam next week too, with the last class (6/22)  going over the final exam.

Since we won’ t have time to review in class, here is what will be covered in the final exam. Students should look at their notes and homework to prepare:

• Congruent triangles and similar triangles;
• Measurement (area and volume) of sectors, cones, pyramids, spheres, areas of similar figures and volumes of similar solids;
• Pythagora’s Theorem
• Basic trigonometry and its applications;
• Motion geometry: reflection, rotation, translation, enlargement, plus their combinations;
• Basic statistics: bar and line graphs, Mode, Mean, and Medians;
• Plynomial addition, subtraction, multiplication and division
• Fractions and fractional equations

We are back to Algebra and go over polynomial addition, subtraction, multiplication, and division.

For addition and subtraction, it is important to remember to combine the terms with the same degrees. For example, you cannot combine a 2x^2 term with 3x term.

For multiplication, remember to multiply every term in one polynomial with every term in the other, then add them all up.

For division, we use the vertical form to do the division. We talk about the relationship between the divident, the divisor, the quotient, and the remainder.

Homework:

Chapter 14 homework: #1 – #17.

We cover reading and drawing of pie chart, line graphs, and pictograms. This is part of Statistics I.

Again, these are topics students feel intuitive and straight forward.

With the extra time, we go over some more of the math contest results.

Homework:

Page 130: #1, 2, 3, 6, 7, 9, 13, 14

We start the 2nd half of the spring semester with focus on statistics, the science about collection and representing data and how to read and draw different graphs.

We first introduce different ways to represent data: bar graph, pie chart, line graph, and pictogram graph. We talk about the pros and cons of each approach.

We then talk about how to read and draw bar charts.

With the extra time left, we talked about a few questions from math contest.

Homework:

P130. #3, 4, 10, 11, 12

We gave back the math contest tests to the students and went over quite some of the questions. There are questions that needs knowledge that we have not taught, but there are many questions that our students should be able to do.

The good news is, it looks like 6 of our students will be in the top to get awards. We are finalizing the list and as soon as the list is finalized, I will let you know.

For the homework, I want to the students to go over the questions 1-10 and the ones we covered in the classroom today, to write down the steps so that they really know how to do them.

School has decided to have a school wide math contest on 4/6/2014 (the midterm exam day) and all Math class students will take part in this contest. We have decided to use the contest in place of the midterm exam.

We will teach today, have the math contest next time, and use the lesson after the contest to go over the contest questions.

Up to now the three kinds of transformations we have talked about: Reflection, Rotation, and Translation, all do not change the figure’s shape and size. They are called rigid transformation. Today we talk about enlargement where the shape remains but the size changes. And an enlargement transformation can increase (when the scale fact is bigger than 1) and reduce (when the scale factor is less than 1) the size. And there must be a center of enlargement.

Lastly, we talked about the combination of multiple transformations and how to identify each transformation involved and fully describe it.

Homework:

Page 122: #14, #15, #17, #18, #19, #20.